Multi-time-scale small-signal modeling method for heterogeneous inverter parallel system

Abstract

The invention discloses a multi-time-scale small-signal modeling method for a heterogeneous inverter parallel system, and belongs to the field of grid-connected inverters. The method comprises the following three steps: firstly, determining a state-space equation considering equal time scales of direct current voltage and alternating current based on a heterogeneous inverter parallel system topology; secondly, performing linearization processing on the nonlinear link to obtain a trajectory linearization equation corresponding to the main circuit and the controller part; and finally, unifying the system coordinate system and the control coordinate system to obtain a linear period time-varying model of the whole closed-loop system. Compared with an existing modeling method, the method has the advantages that conventional analysis can be performed on the heterogeneous system under different power grid intensities, and the action rule of the asymmetric power grid voltage and the system resonant frequency can be described, so that the stability analysis level of the heterogeneous multi-inverter grid-connected system under the complex power grid working condition is improved.

Description

Technical Field

[0001] The present invention belongs to the field of grid-connected inverters, and in particular relates to a multi-time-scale small signal modeling method for a heterogeneous inverter parallel system. Background Art

[0002] The large-scale development and utilization of new energy is essential for ensuring national energy security and achieving the strategic goals of "dual carbon." The rapid development of new energy and the widespread application of power electronics are driving the transformation of power systems toward a high proportion of renewable energy and power electronics. These "double highs" have become a defining characteristic of this new power system.

[0003] In new power systems, inverters serve as the "bridge" between renewable energy and the grid, making them crucial for the safe and stable integration of renewable energy into the grid. Due to the inverse distribution of wind energy and electricity loads in my country, renewable energy sources are mostly connected to the end of the grid, making weak grids the primary form of renewable energy access. Furthermore, grid-connected inverters have the ability to construct voltage / frequency for weak grids, effectively improving the safe and stable operation of weak grids and making them more suitable for grid-connected applications with a high proportion of renewable energy generation. However, taking grid-connected inverters into account, the renewable energy grid-connected system will be presented as a heterogeneous system with both grid-connected and grid-following inverters. However, due to the diverse application conditions, circuit topologies, and control strategies of heterogeneous inverter parallel systems, the analysis of resonance issues in multi-inverter systems becomes more difficult.

[0004] State-space modeling and impedance modeling are currently the most commonly used approaches for multi-machine parallel systems. Both state-space and impedance analysis methods require first establishing a linear time-invariant (LTI) model of the system. Since AC systems do not have a fixed operating point, small-signal analysis methods used for DC systems cannot be directly applied to AC systems. Therefore, a conversion to a two-phase rotating (dq) coordinate system is required to convert fundamental sinusoidal quantities into DC quantities. It should be noted that heterogeneous multi-machine systems involve multiple time scales, including rotor speed, DC voltage, and AC current. Traditional modeling and analysis methods, such as impedance analysis and state-space methods, struggle to accurately characterize the interactive coupling and dynamic characteristics of heterogeneous systems, and cannot be extended to more complex grid conditions.

[0005] In summary, in order to accurately analyze the stability problem of multi-inverter grid-connected systems, a multi-time-scale small signal modeling method for heterogeneous inverter parallel systems is urgently needed to meet the dynamic and steady-state characteristics research of heterogeneous multi-machine parallel systems. Summary of the Invention

[0006] The purpose of the present invention is to address the shortcomings of existing methods and provide a multi-time-scale small signal modeling method for heterogeneous inverter parallel systems. It can not only perform conventional analysis of heterogeneous systems under different grid strengths, but also characterize the effects of grid voltage asymmetry and system resonant frequency, thereby improving the stability analysis level of heterogeneous multi-inverter grid-connected systems under complex grid conditions.

[0007] The object of the present invention is achieved through the following technical solution: a multi-time-scale small signal modeling method for a heterogeneous inverter parallel system, comprising the following steps:

[0008] (1) Determine the state equations for a heterogeneous inverter parallel system that includes both grid-following and grid-forming inverters;

[0009] (2) Establish the trajectory linearization equations of the state space equations of the main circuit and controller;

[0010] (3) Unify the grid coordinate system, phase-locked loop coordinate system, and power outer loop coordinate system to form a linear periodic time-varying model of the complete closed-loop system under multiple time scales.

[0011] Furthermore, the step (1) includes:

[0012] Based on the LC filter of the grid-type / hybrid inverter and the grid-side equivalent circuit, the main circuit state equation of the heterogeneous inverter is established in the αβ coordinate system:

[0013]

[0014] Where, the superscript t represents the system coordinate system, the subscript αβ represents the variables in the two-phase stationary coordinate system; dt is the time differential, L is the filter inductor, C is the filter capacitor, and R C is the parasitic resistance of the filter capacitor, L g is the equivalent inductance of the power grid, R g is the equivalent resistance of the power grid, i L11 、i L12 They are the inductor currents of grid-following and grid-forming inverters, u inv1 、u inv2 are the output voltages of grid-following and grid-forming inverters, i L21 、i L22 are the output currents of the grid-following and grid-forming inverters, u C1 、u C2 are the filter capacitor voltages of the grid-following and grid-forming inverters, i g is the grid-connected current, u g is the grid voltage.

[0015] Based on the topological structure of the control link, the state space equations of the phase-locked loop, current loop, power loop, and voltage-current dual closed loop in the dq coordinate system are determined respectively:

[0016]

[0017]

[0018] Among them, the superscript c represents the control coordinate system, the superscript * represents the reference value of the control parameter, the subscripts d and q represent the variables in the rotating coordinate system, and x PLL is the state variable of the phase-locked loop, θ PLL is the output angle of the phase-locked loop, x d 、x q are the d-axis and q-axis state variables output by the current loop, θ PSL is the output angle of the droop ring, x dv 、x qv They are the d-axis and q-axis state variables of the voltage loop in the voltage-current double closed loop, respectively. di 、x qi are the d-axis and q-axis state variables of the current loop in the voltage and current double closed loop, u d 、u q are the d-axis and q-axis output voltages of the current loop, K ppll , K ipll K is the proportional coefficient and integral coefficient of the phase-locked loop. p , K i is the proportional coefficient and integral coefficient of the current loop, K pv , K iv is the proportional coefficient and integral coefficient of the voltage loop, K ii is the integral coefficient of the current loop in the double closed loop, K c is the active damping feedback coefficient, I c1 is the capacitor current of the grid-following inverter, u pcc is the grid coupling point voltage, M and N are the active-frequency and reactive-voltage droop coefficients of droop control, P ref With Q ref is the active and reactive reference frequency, U ref Generates voltage for droop control, U m is the voltage amplitude, ω ref is the reference angular frequency, and f0 is the fundamental frequency.

[0019] Furthermore, the step (2) includes:

[0020] Based on the state space equations of the main circuit and controller of the heterogeneous inverter parallel system, small signal linearization processing is performed on the time-varying periodic trajectory to obtain the trajectory linearization equation, which is expressed as:

[0021]

[0022] Where Δ represents the change, and the subscript 0 represents the steady-state value of the parameter.

[0023] Furthermore, the step (2) includes:

[0024] (3.1) Linearize the nonlinear relationship equations containing trigonometric functions in the Park coordinate transformation process;

[0025] (3.2) Transform the parameters in the control coordinate system into the system coordinate system, unify the system coordinate system and the control coordinate system, and form the trajectory linearization equation in the system coordinate system;

[0026] (3.3) Based on step (3.2), all variables can be unified into the system coordinate system to form a linear periodic time-varying model of the complete closed-loop system under multiple time scales taking into account DC voltage and AC current.

[0027] The present invention also provides an electronic device comprising a memory and a processor, wherein the memory is coupled to the processor; wherein the memory is used to store program data, and the processor is used to execute the program data to implement the above-mentioned multi-time-scale small signal modeling method for a heterogeneous inverter parallel system.

[0028] The present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-mentioned multi-time-scale small signal modeling method for a heterogeneous inverter parallel system.

[0029] The present invention also provides a computer program product, including a computer program, which, when executed by a processor, implements the above-mentioned multi-time-scale small signal modeling method for a heterogeneous inverter parallel system.

[0030] Compared with the existing methods, the beneficial effects of the present invention are: a multi-time-scale small signal modeling method for a heterogeneous inverter parallel system described in the present invention fully considers the influencing factors such as the interaction of the control links and the multi-time-scale characteristics of the heterogeneous inverter parallel system, and can analyze the periodic time variables in the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for the description. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0032] Figure 1Schematic diagram of the topology of a heterogeneous inverter parallel system;

[0033] Figure 2 The control link topology diagram of the grid-following inverter and the grid-forming inverter;

[0034] Figure 3 The figure is a comparison of the time domain responses of the DC signal of the detailed model and the model proposed in the present invention under step disturbance;

[0035] Figure 4 The figure is a comparison of the time domain responses of the AC signal of the detailed model and the model proposed in the present invention under step disturbance;

[0036] Figure 5 A comparison diagram of the time domain responses of the detailed model and the model proposed in the present invention under the condition of asymmetric grid voltage;

[0037] Figure 6 Root locus diagram of different reactive droop coefficients analyzed by the model proposed in this invention;

[0038] Figure 7 Analyze the root locus diagram of the model proposed in this invention under different power grid strengths;

[0039] Figure 8 The root locus diagram of the model proposed in this invention to analyze the influence of resonant frequency on system stability;

[0040] Figure 9 The grid-connected voltage, current and power waveforms of the heterogeneous inverter parallel system under different reactive droop coefficients;

[0041] Figure 10 The grid-connected voltage, current and power waveforms of the heterogeneous inverter parallel system under different grid strengths;

[0042] Figure 11 Provide output waveforms and FFT analysis of heterogeneous inverter parallel systems at different resonant frequencies;

[0043] Figure 12 This is a schematic diagram of an electronic device provided by the present invention. DETAILED DESCRIPTION

[0044] In order to describe the present invention in more detail, the present invention will be further explained below with reference to the accompanying drawings and implementation examples.

[0045] This paper presents a multi-timescale small-signal modeling method for a heterogeneous parallel inverter system. This method fully considers factors such as the interaction between control links and the multi-timescale characteristics of the heterogeneous parallel inverter system, and is capable of analyzing periodic time-varying variables in the system. The method includes three steps: first, determining the state equations for the heterogeneous parallel inverter system, including both grid-following and grid-forming inverters; second, establishing trajectory linearization equations for the state-space equations of the main circuit and controller; and third, unifying the grid coordinate system, the phase-locked loop coordinate system, and the power outer loop coordinate system to form a linear periodic time-varying model of the complete closed-loop system at multiple time scales, including DC voltage and AC current.

[0046] (1) Specific process of step 1:

[0047] based on Figure 1 The topology of a heterogeneous parallel inverter system is shown in Figure 1. This topology takes into account the phase-locked loop (PLL), current loop, droop control loop, and voltage-current dual closed loops. It is worth noting that in a grid-connected inverter, if the switching frequency is sufficiently high, the switching action does not affect the state evolution, and the inverter model can be simplified to a proportional amplifier with an amplification factor of 1. Based on this assumption, to reduce the order of the equations and the complexity of the modeling, the modeling of the modulation signal is ignored. Furthermore, due to the dynamic performance of the PLL and power loop, the system coordinate system no longer coincides with the control coordinate system. Therefore, the main circuit and control link are modeled in the αβ coordinate system and the dq coordinate system, respectively.

[0048] Based on the LC filter of the grid-type inverter and the grid-side equivalent circuit, the main circuit state equation of the heterogeneous inverter is established in the αβ coordinate system. The main circuit state equation can be expressed as:

[0049]

[0050] Where, the superscript t represents the system coordinate system, the subscript αβ represents the variables in the two-phase stationary coordinate system, dt is the time differential, L is the filter inductor, C is the filter capacitor, and R C is the parasitic resistance of the filter capacitor, L g is the equivalent inductance of the power grid, R g is the equivalent resistance of the power grid, i L11 、i L12 They are the inductor currents of grid-following and grid-forming inverters, u inv1 、u inv2 are the output voltages of grid-following and grid-forming inverters, i L21 、i L22 are the output currents of the grid-following and grid-forming inverters, u C1 、u C2 are the filter capacitor voltages of the grid-following and grid-forming inverters, i g is the grid-connected current, u gis the grid voltage.

[0051] Figure 2 The control link topology diagrams for the grid-following inverter and the grid-forming inverter are shown below. Based on the topological structure of the control link, the state space equations for the phase-locked loop, current loop, power loop, and voltage-current dual closed loop in the dq coordinate system are determined. The state space equations are expressed as follows:

[0052]

[0053] In the formula, the superscript c represents the control coordinate system, the superscript * represents the reference value of the control parameter, the subscripts d and q represent the variables in the rotating coordinate system, and x PLL is the state variable of the phase-locked loop, θ PLL is the output angle of the phase-locked loop, x d 、x q are the d-axis and q-axis state variables output by the current loop, θ PSL is the output angle of the droop ring, x dv 、x qv They are the d-axis and q-axis state variables of the voltage loop in the voltage-current double closed loop, respectively. di 、x qi are the d-axis and q-axis state variables of the current loop in the voltage and current double closed loop, u d 、u q are the d-axis and q-axis output voltages of the current loop, K ppll , K ipll K is the proportional coefficient and integral coefficient of the phase-locked loop. p , K i is the proportional coefficient and integral coefficient of the current loop, K pv , K iv is the proportional coefficient and integral coefficient of the voltage loop, K ii is the integral coefficient of the current loop in the double closed loop, K c is the active damping feedback coefficient, I c1 is the capacitor current of the grid-following inverter, u pcc is the grid coupling point voltage, M and N are the active-frequency and reactive-voltage droop coefficients of droop control, P ref With Q ref is the active and reactive reference frequency, U ref Generates voltage for droop control, U m is the voltage amplitude, ω ref is the reference angular frequency, and f0 is the fundamental frequency.

[0054] (2) Specific process of step 2:

[0055] Based on the state-space equations for the main circuit and controller of the heterogeneous inverter parallel system obtained in step 1, small-signal linearization is performed on the time-varying periodic trajectory to obtain its trajectory linearization equation. The linearized equations for the system's main circuit and control links (phase-locked loop, droop loop, power loop, and voltage-current dual closed loop) can be expressed as:

[0056]

[0057] Where the symbol Δ represents the corresponding linearized variable of the above state variables.

[0058] Since the grid voltage u g is essentially constant, so its value is zero during the linearization process.

[0059] (3) Specific process of step three:

[0060] (3.1) Linearize the nonlinear relationship equation containing trigonometric functions in the Park coordinate transformation link. The trajectory linearization equation of the Park coordinate transformation link can be expressed as:

[0061]

[0062] Where θ is the phase angle of the control link output, which is the phase-locked loop output angle θ mentioned above. PLL and droop control output angle θ PSL , subscript 0 indicates the steady-state value of the parameter.

[0063] (3.2) The parameters in the control coordinate system are transformed into the system coordinate system, and the system coordinate system and the control coordinate system are unified to form the trajectory linearization equation in the system coordinate system. The transformation relationship can be expressed as:

[0064]

[0065] Where a refers to all state variables, and its subscripts d, q, α, and β correspond to the d-axis, q-axis, α-axis, and β-axis components;

[0066] Based on formula (10), the formula (7) Can be transformed into the system coordinate system:

[0067]

[0068] In the formula, all variables are completely expressed by parameters in the system coordinate system. The parameters in other control coordinate systems are deduced in the same way, thus achieving the unification of the system coordinate system and the control coordinate system.

[0069] (3.3) Based on step (3.2), all variables can be unified into the system coordinate system, forming a linear periodic time-varying model of the complete closed-loop system under multiple time scales taking into account DC voltage and AC current. This model can also be expressed as a generalized linear periodic time-varying state matrix:

[0070]

[0071] In the formula Represents the change of the first-order derivative of the state variable, Δx(t) represents the state change, x(t) represents the state variable, u(t) represents the input variable, Δu(t) represents the input change, A(t) and B(t) are time-varying parameter matrices.

[0072] The above steps (1), (2), and (3) together constitute a multi-time-scale small-signal modeling method for a heterogeneous inverter parallel system of the present invention. According to the example parameters provided in Table 1, based on a heterogeneous inverter grid-connected system consisting of a grid-following inverter and a grid-connecting inverter, the accuracy and effectiveness of the small-signal modeling method are analyzed.

[0073] Table 1 Example parameters

[0074]

[0075]

[0076] Figure 3 The time domain response comparison diagram of the DC signal of the detailed model and the model proposed in this invention under step disturbance is shown, and the dynamic response output I of the grid-following inverter and the grid-forming inverter in the system is observed respectively. gdL , I gdM , it can be concluded that the constructed model has a higher accuracy for DC signals.

[0077] Figure 4 The time domain response comparison diagram of the AC signal of the detailed model and the model proposed in this invention under step disturbance is shown, respectively observing the dynamic response output U of the common coupling point voltage and grid current in the parallel system. pccα , I gα , it can be concluded that the constructed model has a high accuracy for AC signals.

[0078] Figure 5 The time domain response comparison diagram of the detailed model and the proposed model under the condition of asymmetric grid voltage is shown in Figure 2. The voltage U at the common coupling point in the parallel system is observed. pccα 、U pccβ , it can be concluded that the established model still has high accuracy under the condition of asymmetric grid voltage.

[0079] Figure 6This is the root locus plot for different reactive power coefficients in the proposed model analysis droop power loop. The reactive power droop coefficient N gradually increases from 0.001 to 0.02. Characteristic root analysis results show that the maximum real part of the system's characteristic exponent increases with increasing reactive power droop coefficient N, leading to instability. When N = 0.02, the system becomes unstable. Excessive reactive power droop coefficient N reduces system stability. The theoretical analysis results are consistent with those of traditional modeling.

[0080] Figure 7 The proposed model analyzes the root locus plot for different grid strengths, SCRs. The system grid strength decreases from 3 to 2, and the grid operating condition changes from a strong grid to a weak grid. Characteristic root analysis results show that when the system short-circuit ratio (SCR) is 2 ≤ SCR ≤ 3, the heterogeneous parallel system remains stable due to the complementary stability of the grid-following and grid-forming inverters under strong and weak grid conditions. The theoretical analysis results are consistent with those of traditional modeling.

[0081] Figure 8 This is a root locus plot of the proposed model analyzing the effect of resonant frequency on system stability. As the resonant frequency of the simulated system increases from 0 Hz to 20 Hz, the system is at risk of subsynchronous oscillation. Eigenvalue root analysis results show that due to the inherent inertia strength of heterogeneous systems, the parallel system can remain stable even with low low-frequency resonance content. The theoretical analysis results are consistent with those of traditional modeling.

[0082] To better demonstrate the effectiveness of the proposed method, a simulation example is presented below. The simulation parameters are shown in Table 1. A heterogeneous inverter parallel system is constructed using two types of inverters. To verify the effectiveness and accuracy of the proposed modeling method, a simulation platform was built in MATLAB / Simulink.

[0083] Figure 9 is the grid-connected voltage U of the heterogeneous inverter parallel system under different reactive droop coefficients pcc , grid-connected current I g , active power P, and reactive power Q. The simulation results show that the system tends to become unstable as the reactive power droop coefficient N increases. When N = 0.02, the system becomes unstable. Further increasing the reactive power droop coefficient to 0.025 still results in system instability. The simulation results are consistent with the theoretical analysis above, demonstrating the accuracy of the proposed modeling.

[0084] Figure 10 is the grid-connected voltage U of the heterogeneous inverter parallel system under different grid strength SCR pcc , grid-connected current I g, active power P, and reactive power Q. The simulation results show that when the system short-circuit ratio is 2 ≤ SCR ≤ 3, the heterogeneous parallel system remains stable. These simulation results are consistent with the theoretical analysis above, demonstrating the accuracy of the proposed model.

[0085] Figure 11 is the grid-connected voltage U of the heterogeneous inverter parallel system at different resonant frequencies pcc , grid-connected current I g Simulation waveforms and corresponding FFT analysis. The simulation results show that the parallel system remains stable regardless of the original operating conditions or when low-frequency components (10Hz and 20Hz) are present. The simulation results are consistent with the above analysis, demonstrating that the proposed model is accurate.

[0086] In summary, this paper proposes a multi-timescale small-signal modeling method for heterogeneous parallel inverter systems. Compared to existing methods, this method is innovative in that it fully considers factors such as the interaction between control links and the multi-timescale characteristics of the heterogeneous parallel inverter system, and can analyze periodic time-varying variables in the system. This method not only enables conventional analysis of heterogeneous systems under different short-circuit ratios, but also characterizes the effects of grid voltage asymmetry and system resonant frequency, thereby improving the stability analysis of heterogeneous multi-inverter grid-connected systems under complex grid conditions.

[0087] Figure 12 This is a schematic diagram of the structure of an electronic device provided by an embodiment of the present invention. Figure 12 The electronic device provided in this embodiment includes: a memory and a processor, wherein the memory is used to store information including program instructions, and the processor is used to control the execution of the program instructions. When the program instructions are loaded and executed by the processor, the above-mentioned multi-time-scale small signal modeling method of a heterogeneous inverter parallel system is implemented.

[0088] It should be noted that, in addition to Figure 12 In addition to the memory and processor shown, the electronic device may also include other hardware according to its actual functions, which will not be described in detail.

[0089] The present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-mentioned multi-time-scale small signal modeling method for a heterogeneous inverter parallel system.

[0090] The present invention also provides a computer program product, including a computer program, which, when executed by a processor, implements the above-mentioned multi-time-scale small signal modeling method for a heterogeneous inverter parallel system.

[0091] Those skilled in the art will appreciate that the embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the present application can adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application can adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) that contain computer-usable program code.

[0092] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the steps in the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0093] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0094] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0095] The above embodiments are intended only to illustrate the design concepts and features of the present invention. Their purpose is to enable those skilled in the art to understand the contents of the present invention and implement them accordingly. The scope of protection of the present invention is not limited to the above embodiments. Therefore, any equivalent changes or modifications made based on the principles and design concepts disclosed in the present invention are within the scope of protection of the present invention.

Claims

1. A multi-time-scale small signal modeling method for a heterogeneous inverter parallel system, characterized in that: The following steps are involved: (1) Determine the state equations for a heterogeneous inverter parallel system that includes both grid-following and grid-forming inverters; (2) Establish the trajectory linearization equations of the state space equations of the main circuit and controller; (3) Unify the grid coordinate system, phase-locked loop coordinate system, and power outer loop coordinate system to form a linear periodic time-varying model of the complete closed-loop system under multiple time scales.

2. The method according to claim 1, characterized in that The step (1) comprises: Based on the LC filter of the grid-type / hybrid inverter and the grid-side equivalent circuit, the main circuit state equation of the heterogeneous inverter is established in the αβ coordinate system: Wherein, the superscript t represents the system coordinate system, the subscript αβ represents the variables in the two-phase stationary coordinate system, dt is the time differential, L is the filter inductor, C is the filter capacitor, R C is the parasitic resistance of the filter capacitor, L g is the equivalent inductance of the power grid, R g is the equivalent resistance of the power grid, i L11 、i L12 They are the inductor currents of grid-following and grid-forming inverters, u inv1 、u inv2 are the output voltages of grid-following and grid-forming inverters, i L21 、i L22 are the output currents of the grid-following and grid-forming inverters, u C1 、u C2 are the filter capacitor voltages of the grid-following and grid-forming inverters, i g is the grid-connected current, u g is the grid voltage; Based on the topological structure of the control link, the state space equations of the phase-locked loop, current loop, power loop, and voltage-current dual closed loop in the dq coordinate system are determined respectively: Among them, the superscript c represents the control coordinate system, the superscript * represents the reference value of the control parameter, the subscripts d and q represent the variables in the rotating coordinate system, and x PLL is the state variable of the phase-locked loop, θ PLL is the output angle of the phase-locked loop, x d 、x q are the d-axis and q-axis state variables output by the current loop, θ PSL is the output angle of the droop ring, x dv 、x qv They are the d-axis and q-axis state variables of the voltage loop in the voltage-current double closed loop, respectively. di 、x qi are the d-axis and q-axis state variables of the current loop in the voltage and current double closed loop, u d 、u q are the d-axis and q-axis output voltages of the current loop, K ppll , K ipll K is the proportional coefficient and integral coefficient of the phase-locked loop. p , K i is the proportional coefficient and integral coefficient of the current loop, K pv , K iv is the proportional coefficient and integral coefficient of the voltage loop, K ii is the integral coefficient of the current loop in the double closed loop, K c is the active damping feedback coefficient, I c1 is the capacitor current of the grid-following inverter, u pcc is the grid coupling point voltage, M and N are the active-frequency and reactive-voltage droop coefficients of droop control, P ref With Q ref is the active and reactive reference frequency, U ref Generates voltage for droop control, U m is the voltage amplitude, ω ref is the reference angular frequency, and f0 is the fundamental frequency.

3. The method according to claim 2, characterized in that The step (2) comprises: Based on the state space equations of the main circuit and controller of the heterogeneous inverter parallel system, small signal linearization processing is performed on the time-varying periodic trajectory to obtain the trajectory linearization equation, which is expressed as: Where Δ represents the change, and the subscript 0 represents the steady-state value of the parameter.

4. The method according to claim 3, characterized in that The step (2) comprises: (3.1) Linearize the nonlinear relationship equations containing trigonometric functions in the Park coordinate transformation process; (3.2) Transform the parameters in the control coordinate system into the system coordinate system, unify the system coordinate system and the control coordinate system, and form the trajectory linearization equation in the system coordinate system; (3.3) Based on step (3.2), all variables can be unified into the system coordinate system to form a linear periodic time-varying model of the complete closed-loop system under multiple time scales taking into account DC voltage and AC current.

5. An electronic device comprising a memory and a processor, characterized in that: The memory is coupled to the processor; wherein the memory is used to store program data, and the processor is used to execute the program data to implement a multi-time-scale small signal modeling method for a heterogeneous inverter parallel system as described in any one of claims 1-4 above.

6. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, a multi-time-scale small-signal modeling method for a heterogeneous inverter parallel system is implemented as described in claims 1-4.

7. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, the method for multi-time-scale small signal modeling of a heterogeneous inverter parallel system described in claims 1-4 is implemented.

Images